Question 4# Read the following algorithm: Algorithm for converting a fraction a into binary with p binary places. Inputs: fraction z EQ, 0
Question 4# Read the following algorithm: Algorithm for converting a fraction a into binary with p binary places. Inputs: fraction z EQ, 0
Chapter3: Data Representation
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Problem 15VE: The result of adding, subtracting, or multiplying two integers might result in overflow but never...
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![Question 4# Read the following algorithm:
Algorithm for converting a fraction into binary with p binary places.
Inputs: fraction r EQ, 0<x< 1 and number of places p E N.
Outputs: bits b₁,b2,..., bp such that (0.bybą... bp)2 is the
best approximation to z using p binary places.
Method:
Initialise: j1, b₁,b2,...,bp0
Loop: if j = p + 1 stop.
x + 2x
If r≥1 [b, 1, x-x-1]
j+j+1
Repeat loop
(a) Verify that the algorithm converts to 0.11010, when p=5. Can you spot how to
express exactly in repeating binary?
(b) Express 0.8510 as accurately as possible with 8 binary places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe76b03dc-a295-41f1-af21-0d00d1072650%2Fabec96fd-20db-47ab-bcc9-21d830244acf%2Ftsmtf6v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 4# Read the following algorithm:
Algorithm for converting a fraction into binary with p binary places.
Inputs: fraction r EQ, 0<x< 1 and number of places p E N.
Outputs: bits b₁,b2,..., bp such that (0.bybą... bp)2 is the
best approximation to z using p binary places.
Method:
Initialise: j1, b₁,b2,...,bp0
Loop: if j = p + 1 stop.
x + 2x
If r≥1 [b, 1, x-x-1]
j+j+1
Repeat loop
(a) Verify that the algorithm converts to 0.11010, when p=5. Can you spot how to
express exactly in repeating binary?
(b) Express 0.8510 as accurately as possible with 8 binary places.
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